Expand the product ${(x+3)(x-8)}$.
Solution: When using the distributive property for the first time, we add the product of $x+3$ and $x$ to the product of $x+3$ and $-8$:

\begin{align*}
(x+3)(x-8) &= (x+5) \cdot x + (x+5) \cdot (-8)\\
&= x(x+3) - 8(x+3)
\end{align*}We use the distributive property again and combine like terms:

\begin{align*}
x(x+3) - 8(x+3) &= x^2 + 3x - 8x - 24\\
&= \boxed{x^2 - 5x - 24}
\end{align*}